# Optimal Differentially Private Sampling of Unbounded Gaussians

arXiv: https://arxiv.org/abs/2503.01766 · HTML: https://mlsanity.com/paper/2503.01766/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 30 of 31)

- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [Differentially Private Synthetic Data via Foundation Model APIs 2: Text](https://mlsanity.com/paper/2403.01749/) (2024)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Robust and Differentially Private Mean Estimation](https://mlsanity.com/paper/2102.09159/) (2021)
- [Differentially Private Synthetic Data via Foundation Model APIs 1: Images](https://mlsanity.com/paper/2305.15560/) (2023)
- [Differential privacy and robust statistics in high dimensions](https://mlsanity.com/paper/2111.06578/) (2021)
- [Private Hypothesis Selection](https://mlsanity.com/paper/1905.13229/) (2019)
- [Don't Generate Me: Training Differentially Private Generative Models with Sinkhorn Divergence](https://mlsanity.com/paper/2111.01177/) (2021)
- [Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation](https://mlsanity.com/paper/1906.02830/) (2019)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Privacy-preserving Prediction](https://mlsanity.com/paper/1803.10266/) (2018)
- [Robustness Implies Privacy in Statistical Estimation](https://mlsanity.com/paper/2212.05015/) (2022)
- [Covariance-Aware Private Mean Estimation Without Private Covariance Estimation](https://mlsanity.com/paper/2106.13329/) (2021)
- [On the Sample Complexity of Privately Learning Unbounded High-Dimensional Gaussians](https://mlsanity.com/paper/2010.09929/) (2020)
- [Private and polynomial time algorithms for learning Gaussians and beyond](https://mlsanity.com/paper/2111.11320/) (2021)
- [Private Robust Estimation by Stabilizing Convex Relaxations](https://mlsanity.com/paper/2112.03548/) (2021)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [A Private and Computationally-Efficient Estimator for Unbounded Gaussians](https://mlsanity.com/paper/2111.04609/) (2021)
- [Private Estimation with Public Data](https://mlsanity.com/paper/2208.07984/) (2022)
- [Pre-trained Perceptual Features Improve Differentially Private Image Generation](https://mlsanity.com/paper/2205.12900/) (2022)
- [From Robustness to Privacy and Back](https://mlsanity.com/paper/2302.01855/) (2023)
- [Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions](https://mlsanity.com/paper/2301.12250/) (2023)
- [Private GANs, Revisited](https://mlsanity.com/paper/2302.02936/) (2023)
- [Better and Simpler Lower Bounds for Differentially Private Statistical Estimation](https://mlsanity.com/paper/2310.06289/) (2023)
- [Private Distribution Learning with Public Data: The View from Sample Compression](https://mlsanity.com/paper/2308.06239/) (2023)
- [Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes](https://mlsanity.com/paper/2404.17714/) (2024)
- [Differentially Private Sampling from Distributions](https://mlsanity.com/paper/2211.08193/) (2022)
- [PLAN: Variance-Aware Private Mean Estimation](https://mlsanity.com/paper/2306.08745/) (2023)
- [On Differentially Private Sampling from Gaussian and Product Distributions](https://mlsanity.com/paper/2306.12549/) (2023)

## Built on by (most cited first, 1 of 1)

- [Locally Optimal Private Sampling: Beyond the Global Minimax](https://mlsanity.com/paper/2510.09485/) (2025)

## Abstract (arXiv)

We provide the first widetildeOleft(dright)-sample algorithm for sampling from unbounded Gaussian distributions under the constraint of left(varepsilon, δright)-differential privacy. This is a quadratic improvement over previous results for the same problem, settling an open question of Ghazi, Hu, Kumar, and Manurangsi.